## The perimeter of a rectangle is 108cm. The ration of its length to its width is 7:2 what is the area of the rectangle in cm2?

Question

The perimeter of a rectangle is 108cm. The ration of its length to its width is 7:2 what is the area of the rectangle in cm2?

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Mathematics
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2021-07-22T11:36:14+00:00
2021-07-22T11:36:14+00:00 1 Answers
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## Answers ( )

Answer:504 cm²

Step-by-step explanation:Let the length and the width of the rectangle be L cm and W cm respectively.

Perimeter= 2(L +W)

2(L +W)= 108

L +W= 108 ÷2

L +W= 54

L= 54 -W —–(1)

Cross multiply:2L= 7W —–(2)

Substitute (1) into (2):

2(54 -W)= 7W

Expand:108 -2W= 7W

+2W on both sides:9W= 108

Divide both sides by 9:W= 108 ÷9

W= 12

Substitute W= 12 into (1):L= 54 -12

L= 42

Area of rectangle

= length ×width

= LW

= 42(12)

=

504 cm²